Understand how a low pass filter

In summary, the conversation is about understanding how a low pass filter for a speaker works, with the function \mid H \mid = U_out / U_in and the formula \mid H \mid = R / \sqrt{R^2 + (\omega L)^2}. The person is confused about how the values of frequency f affect the output, with f \rightarrow 0 \Rightarrow \mid H \mid \rightarrow 1 and f \rightarrow \infty \Rightarrow \mid H \mid \rightarrow 0. They realize that a graph would be helpful in understanding this concept.
  • #1
Xiox
15
0
Hi, I'm new into this subject.

I'm trying to understand how a low pass filter (where the frequency f is from 0 Hz to [tex] f_u [/tex] ) for a speacker is working. The fuction for the low pass filter is [tex]\mid H \mid = U_out / U_in[/tex], that is

[tex]\mid H \mid = R / \sqrt{R^2 + ( \omega L )^2}[/tex]

where

[tex] \omega = 2 \pi f [/tex]

That I don't really understand is how [tex]f \rightarrow 0 \Rightarrow \mid H \mid \rightarrow 1 = \mid H \mid_max [/tex] (f is the frequency) and [tex]f \rightarrow \infty \Rightarrow \mid H \mid \rightarrow 0 [/tex]. I believe that I would need a graph.
 
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  • #2
Gm, I've reckoned it out, I quess it was too persceptible to percieve, sorry.
 
  • #3


Sure, I'd be happy to help explain how a low pass filter works. A low pass filter is a type of electronic circuit that allows low frequency signals to pass through while attenuating (decreasing) high frequency signals. This is achieved by using a combination of resistors, capacitors, and inductors. The function you mentioned, \mid H \mid = U_out / U_in, represents the ratio of the output voltage (U_out) to the input voltage (U_in) at a given frequency.

Let's break down the function further to understand how it relates to the behavior of a low pass filter. The term R represents the resistance in the circuit, while the term \omega L represents the reactance (a measure of opposition to the flow of current) of the inductor. As you mentioned, \omega = 2 \pi f, where f is the frequency. This means that as the frequency increases, the reactance of the inductor also increases.

Now, let's look at the two scenarios you mentioned: f \rightarrow 0 and f \rightarrow \infty. When f \rightarrow 0, the reactance of the inductor becomes negligible compared to the resistance, and the function simplifies to \mid H \mid = R / R = 1. This means that at very low frequencies, the output voltage will be essentially the same as the input voltage, and there will be minimal attenuation of the signal. This is why \mid H \mid \rightarrow 1, or approaches its maximum value, at low frequencies.

On the other hand, when f \rightarrow \infty, the reactance of the inductor becomes very large compared to the resistance, and the function simplifies to \mid H \mid = R / \infty = 0. This means that at very high frequencies, the output voltage will be significantly less than the input voltage, and there will be a large attenuation of the signal. This is why \mid H \mid \rightarrow 0, or approaches its minimum value, at high frequencies.

A graph of this function would show a gradual decrease from 1 at low frequencies to 0 at high frequencies, with a cutoff frequency f_u where the output voltage is half the input voltage. This cutoff frequency is determined by the values of the resistance and inductance in the circuit.

I hope this explanation helps you understand how a low pass filter works. Let me know if you have
 

1. What is a low pass filter?

A low pass filter is an electronic circuit that allows low frequency signals to pass through while attenuating high frequency signals. It is used to remove unwanted high frequency noise from a signal.

2. How does a low pass filter work?

A low pass filter works by using a combination of resistors, capacitors, and inductors to create a frequency-dependent voltage divider. This means that the output voltage of the filter will vary depending on the frequency of the input signal.

3. What are the main applications of a low pass filter?

Low pass filters are commonly used in audio systems to remove high frequency noise from music or speech signals. They are also used in communication systems to filter out unwanted high frequency noise from transmitted signals.

4. What is the difference between a passive and an active low pass filter?

A passive low pass filter uses only passive components like resistors, capacitors, and inductors to filter the signal. An active low pass filter, on the other hand, uses an active component like an op-amp to amplify and filter the signal.

5. How do I choose the right cut-off frequency for a low pass filter?

The cut-off frequency of a low pass filter is the frequency at which the signal is attenuated by 3dB. To choose the right cut-off frequency, you need to consider the frequency range of the signal you want to filter and the amount of attenuation you want to achieve for the high frequency noise. Generally, the cut-off frequency is chosen to be slightly lower than the highest frequency of the signal to avoid any distortion.

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